Analysis deals with functions.

Very naively, but sufficient for the purposes of these pages, a set will be defined as a collection of objects of any nature, but here we will focus on real numbers. Given two sets A and B, both nonempty, a function with domain A and range B is a correspondence f that associates elements of set A with elements of set B, such that both of the following conditions are satisfied:

• Every element a of A is associated with an element b of B;

• The element \(b \in B\) associated with element \(a \in A\) is unique.

We will use the notation \(f: A \rightarrow B\) to indicate that f is a function with domain A and range B. Also, we will write \(b = f(a)\) to indicate that b is the unique element of B associated with element \(a \in A\).

The set

formed by all the elements of B that are associated with some element of A, is called the image of the function f.